Related papers: Character sums estimates and an application to a p…

We obtain a new bound of certain double multiplicative character sums. We use this bound together with some other previously obtained results to obtain new algorithms for finding roots of polynomials modulo a prime $p$.

We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.

We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new problem on oscillations of characters on differences between…

We study large values of quadratic character sums with summation lengths exceeding the square root of the modulus. Assuming the Generalized Riemann Hypothesis, we obtain a new Omega result.

We obtain a new bound on certain double sums of multiplicative characters improving the range of several previous results. This improvement comes from new bounds on the number of collinear triples in finite fields, which is a classical…

We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with multiplicative characters to which…

This paper proves Burgess bounds for short mixed character sums in multi-dimensional settings. The mixed character sums we consider involve both an exponential evaluated at a real-valued multivariate polynomial, and a product of…

We prove character sum estimates for additive Bohr subsets modulo a prime. These estimates are analogous to classical character sum bounds of Polya-Vinogradov and Burgess. These estimates are applied to obtain results on recurrence mod $p$…

We obtain nontrivial bounds for character sums with multiplicative and additive characters over finite fields over elements with restricted coordinate expansion. In particular, we obtain a nontrivial estimate for such a sum over a finite…

A classical result of Paley shows that there are infinitely many quadratic characters $\chi\mod{q}$ whose character sums get as large as $\sqrt{q}\log \log q$; this implies that a conditional upper bound of Montgomery and Vaughan cannot be…

A few elementary estimates of a basic character sum over the prime numbers are derived here. These estimates are nontrivial for character sums modulo large q. In addition, an omega result for character sums over the primes is also included.

In this paper we give a refinement of the bound of D. A. Burgess for multiplicative character sums modulo a prime number $q$. This continues a series of previous logarithmic improvements, which are mostly due to H. Iwaniec and E. Kowalski.…

For integer $q$, let $\chi$ be a primitive multiplicative character$\pmod q.$ For integer $a$ coprime to $q$, we obtain a new bound for the sums $$\sum_{n\le N}\Lambda(n)\chi(n+a),$$ where $\Lambda(n)$ is the von Mangoldt function. This…

Let $p$ be a prime. We prove bounds on short Dirichlet character sums evaluated at a class of homogeneous polynomials in arbitrary dimensions. In every dimension, this bound is nontrivial for sums over boxes with side lengths as short as…

We establish new estimates on short character sums for arbitrary composite moduli with small prime factors. Our main result improves on the Graham-Ringrose bound for square free moduli and also on the result due to Gallagher and Iwaniec…

We improve a recent result of B. Hanson (2015) on multiplicative character sums with expressions of the type $a + b +cd$ and variables $a,b,c,d$ from four distinct sets of a finite field. We also consider similar sums with $a + b(c+d)$.…

We obtain transformation formulas for quadratic character sums with quartic and cubic polynomial arguments.

We study additive double character sums over two subsets of a finite field. We show that if there is a suitable rational self-map of small degree of a set $D$, then this set contains a large subset $U$ for which the standard bound on the…

We obtain a Burgess-type bound for character sums over unions of intervals. The result follows from the argument of Heath-Brown, with an improvement in one of the steps.

We estimate mixed character sums of polynomial values over elements of a finite field $\mathbb F_{q^r}$ with sparse representations in a fixed ordered basis over the subfield $\mathbb F_q$. First we use a combination of the…